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Exoplanet Detection Techniques
Debra A. Fischer1, Andrew W. Howard2, Greg P. Laughlin3, Bruce
Macintosh4, SuvrathMahadevan5,6, Johannes Sahlmann7, Jennifer C.
Yee8
We are still in the early days of exoplanet discovery.
Astronomers are beginning to model the atmospheresand interiors of
exoplanets and have developed a deeper understanding of processes
of planet formation andevolution. However, we have yet to map out
the full complexity of multi-planet architectures or to detect
Earthanalogues around nearby stars. Reaching these ambitious goals
will require further improvements in instru-mentation and new
analysis tools. In this chapter, we provide an overview of five
observational techniquesthat are currently employed in the
detection of exoplanets: optical and IR Doppler measurements,
transit pho-tometry, direct imaging, microlensing, and astrometry.
We provide a basic description of how each of thesetechniques works
and discuss forefront developments that will result in new
discoveries. We also highlight theobservational limitations and
synergies of each method and their connections to future space
missions.
Subject headings:
1. Introduction
Humans have long wondered whether other solar sys-tems exist
around the billions of stars in our galaxy. In thepast two decades,
we have progressed from a sample of oneto a collection of hundreds
of exoplanetary systems. Insteadof an orderly solar nebula model,
we now realize that chaosrules the formation of planetary systems.
Gas giant plan-ets can migrate close to their stars. Small rocky
planets areabundant and dynamically pack the inner orbits. Planets
cir-cle outside the orbits of binary star systems. The diversityis
astonishing.
Several methods for detecting exoplanets have been de-veloped:
Doppler measurements, transit observations, mi-crolensing,
astrometry, and direct imaging. Clever innova-tions have advanced
the precision for each of these tech-niques, however each of the
methods have inherent obser-vational incompleteness. The lens
through which we de-tect exoplanetary systems biases the parameter
space thatwe can see. For example, Doppler and transit
techniquespreferentially detect planets that orbit closer to their
hoststars and are larger in mass or size while microlensing,
as-trometry, and direct imaging are more sensitive to planets
inwider orbits. In principle, the techniques are complemen-
1Department of Astronomy, Yale University, New Haven, CT
06520,USA
2Institute for Astronomy, University of Hawai‘i at Manoa, 2680
Wood-lawn Drive, Honolulu, HI 96822, USA
3UCO/Lick Observatory, University of California at Santa Cruz,
SantaCruz, CA 95064, USA
4Stanford University, Palo Alto CA USA5Center for exoplanets and
Habitable Worlds, The Pennsylvania State
University, University Park, PA 16802, USA6Department of
Astronomy and Astrophysics, The Pennsylvania State
University, University Park, PA 16802, USA7Observatoire de
Genève, Université de Genève, 51 Chemin Des Mail-
lettes, 1290 Versoix, Switzerland8Harvard-Smithsonian Center for
Astrophysics, 60 Garden St, Cam-
bridge, MA 02138 USA
tary; in practice, they are not generally applied to the
samesample of stars, so our detection of exoplanet architectureshas
been piecemeal. The explored parameter space of ex-oplanet systems
is a patchwork quilt that still has severalmissing squares.
2. The Doppler Technique
2.1. Historical Perspective
The first Doppler detected planets were met with skep-ticism.
Campbell et al. (1988) identified variations in theresidual
velocities of γ Ceph, a component of a binary starsystem, but
attributed them to stellar activity signals un-til additional data
confirmed this as a planet fifteen yearslater (Hatzes et al.,
2003). Latham et al. (1989) detecteda Doppler signal around HD
114762 with an orbital periodof 84 days and a mass MP sin i =
11MJup. Since the or-bital inclination was unknown, they expected
that the masscould be significantly larger and interpreted their
data as aprobable brown dwarf. When Mayor and Queloz (1995)modeled
a Doppler signal in their data for the sunlike star,51 Pegasi, as a
Jupiter-mass planet in a 4.23-day orbit, as-tronomers wondered if
this could be a previously unknownmode of stellar oscillations
(Gray, 1997) or non-radial pul-sations (Hatzes et al., 1997). The
unexpected detectionof significant eccentricity in exoplanet
candidates furtherraised doubts among astronomers who argued that
althoughstars existed in eccentric orbits, planets should reside in
cir-cular orbits (Black, 1997). It was not until the first
transitingplanet (Henry et al., 2000; Charbonneau et al., 2000)
andthe first multi-planet system (Butler et al., 1999) were
de-tected (almost back-to-back) that the planet interpretationof
the Doppler velocity data was almost unanimously ac-cepted.
The Doppler precision improved from about 10 m s−1 in1995 to 3 m
s−1 in 1998, and then to about 1 m s−1 in 2005when HARPS was
commissioned (Mayor et al., 2003). ADoppler precision of 1 m s−1
corresponds to shifts of stellar
1
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1985 1990 1995 2000 2005 2010 2015Year of Discovery
10-3
10-2
10-1
100
101Pl
anet
ary
Mas
s [M
Jup]
Earth
Neptune
Jupiter
Fig. 1.— Planet mass is plotted as a function of the yearof
discovery. The color coding is gray for planets with noknown
transit, whereas light red is planets that do transit.
lines across 1/1000th of a CCD pixel. This is a challeng-ing
measurement that requires high signal-to-noise, high-resolution,
and large spectral coverage. Echelle spectrome-ters typically
provide these attributes and have served as theworkhorse
instruments for Doppler planet searches.
Figure 1 shows the detection history for planets identi-fied
with Doppler surveys (planets that also are observedto transit
their host star are color-coded in red). The firstplanets were
similar in mass to Jupiter and there has beena striking decline in
the lower envelope of detected planetmass with time as
instrumentation improved.
2.2. Radial Velocity Measurements
The Doppler technique measures the reflex velocity thatan
orbiting planet induces on a star. Because the
star-planetinteraction is mediated by gravity, more massive planets
re-sult in larger and more easily detected stellar velocity
am-plitudes. It is also easier to detect close-in planets,
bothbecause the gravitational force increases with the square ofthe
distance and because the orbital periods are shorter andtherefore
more quickly detected. Lovis and Fischer (2011)provide a detailed
discussion of the technical aspects ofDoppler analysis with both an
iodine cell and a thorium-argon simultaneous reference source.
The radial velocity semi-amplitude,K1 of the star can
beexpressed in units of cm s−1 with the planet mass in unitsof
M⊕:
K∗=8.95 cm s−1√
1−e2MP sin i
M⊕
(M∗+MPM�
)−2/3(P
yr
)−1/3(1)
The observed parameters (velocity semi-amplitude K∗,orbital
period P , eccentricity e, and orientation angle ω) areused to
calculate a minimum mass of the planet MP sin i ifthe mass of the
star M∗ is known. The true mass of the
Fig. 2.— The phase-folded data for the detection of a
planetorbiting HD 85512 (Figure 13 from Pepe et al. 2011).
planet is unknown because it is modulated by the
unknowninclination. For example, if the orbital inclination is
thirtydegrees, the true mass is a factor of two times the
Doppler-derived MP sin i. The statistical probability that the
orbitinclination is within an arbitrary range i1 < i < i2 is
givenby
Pincl = | cos(i2)− cos(i1)| (2)
Thus, there is a roughly 87% probability that randomorbital
inclinations are between thirty and ninety degrees, orequivalently,
an 87% probability that the true mass is withina factor of two of
the minimum mass MP sin i.
Radial velocity observations must cover one completeorbit in
order to robustly measure the orbital period. As aresult the first
detected exoplanets resided in short-periodorbits. Doppler surveys
that have continued for a decade ormore (Fischer et al., 2013;
Marmier et al., 2013) have beenable to detect gas giant planets in
Jupiter-like orbits.
2.3. The floor of the Doppler precision
An important question is whether the Doppler techniquecan be
further improved to detect smaller planets at widerorbital radii.
The number of exoplanets detected each yearrose steadily until 2011
and has dropped precipitously afterthat year. This is due in part
to the fact that significant tele-scope time has been dedicated to
transit follow-up and alsobecause observers are working to extract
the smallest pos-sible planets, requiring more Doppler measurement
pointsgiven current precision. Further gains in Doppler
precisionand productivity will require new instruments with
greaterstability as well as analytical techniques for
decorrelatingstellar noise.
Figure 2, reproduced from Pepe et al. (2011), shows anexample of
one of the lowest amplitude exoplanets, detectedwith HARPS. The
velocity semi-amplitude for this planet isK = 0.769 m s−1 and the
orbital period is 58.43 days. Thedata was comprised of 185
observations spanning 7.5 years.The residual velocity scatter after
fitting for the planet wasreported to be 0.77 m s−1, showing that
high precision can
2
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be achieved with many data points to beat down the
singlemeasurement precision.
One promising result suggests that it may be possiblefor stable
spectrometers to average over stellar noise sig-nals and reach
precisions below 0.5 m s−1, at least for somestars. After fitting
for three planets in HD20794, Pepeet al. (2011) found that the RMS
of the residual veloci-ties decreased from 0.8 m s−1 to 0.2 m s−1
as they binnedthe data in intervals from 1 to 40 nights. Indeed, a
yearlater, the HARPS team published the smallest velocity sig-nal
ever detected: a planet candidate that orbits alpha Cen-tauri B
(Dumusque et al., 2012) with a velocity amplitudeK = 0.51 m s−1,
planet mass M sin i = 1.13M⊕, andan orbital period of 3.24 days.
This detection required 469Doppler measurements obtained over 7
years and fit for sev-eral time-variable stellar noise signals.
Thus, the number ofobservations required to solve for the
5-parameter Keple-rian model increases exponentially with
decreasing velocityamplitude.
2.4. The Future of Doppler Detections
It is worth pondering whether improved instruments withhigher
resolution, higher sampling, greater stability andmore precise
wavelength calibration will ultimately be ableto detect analogs of
the Earth with 0.1 m s−1 velocity am-plitudes. An extreme precision
spectrometer will have strin-gent environmental requirements to
control temperature,pressure and vibrations. The dual requirements
of high res-olution and high signal-to-noise lead to the need for
mod-erate to large aperture telescopes (Strassmeier et al.,
2008;Spanò et al., 2012). The coupling of light into the
instru-ment must be exquisitely stable. This can be achieved witha
double fiber scrambler (Hunter and Ramsey, 1992) wherethe near
field of the input fiber is mapped to the far fieldof the output
fiber, providing a high level of scramblingin both the radial and
azimuthal directions. At some costto throughput, the double fiber
scrambler stabilizes varia-tions in the spectral line spread
function (sometimes calleda point spread function) and produces a
series of spectrathat are uniform except for photon noise. Although
thefibers provide superior illumination of the spectrometer
op-tics, some additional care in the instrument design phase
isrequired to provide excellent flat fielding and sky subtrac-tion.
The list of challenges to extreme instrumental pre-cision also
includes the optical CCD detectors, with intra-pixel quantum
efficiency variations, tiny variations in pixelsizes, charge
diffusion and the need for precise controllersoftware to perfectly
clock readout of the detector.
In addition to the instrumental precision, another chal-lenge to
high Doppler precision is the star itself. Stellaractivity,
including star spots, p-mode oscillations and vari-able granulation
are tied to changes in the strength of stellarmagnetic fields.
These stellar noise sources are sometimescalled stellar jitter and
can produce line profile variationsthat skew the center of mass for
a spectral line in a way thatis (mis)interpreted by a Doppler code
as a velocity change
in the star. Although stellar noise signals are subtle,
theyaffect the spectrum in a different way than dynamical
ve-locities. The stellar noise typically has a color dependenceand
an asymmetric velocity component. in order to reachsignificantly
higher accuracy in velocity measurements, itis likely that we will
need to identify and model or decorre-late the stellar noise.
3. Infrared Spectroscopy
3.1. Doppler Radial Velocities in the Near Infrared
The high fraction of Earth-size planets estimated to or-bit in
the habitable zones (HZs) of M dwarfs (Dressing andCharbonneau,
2013; Kopparapu, 2013; Bonfils et al., 2013)makes the low mass
stars very attractive targets for DopplerRV surveys. The lower
stellar mass of the M dwarfs, aswell as the short orbital periods
of HZ planets, increasesthe amplitude of the Doppler wobble (and
the ease of its de-tectability) caused by such a terrestrial-mass
planet. How-ever, nearly all the stars in current optical RV
surveys areearlier in spectral type than ∼M5 since later spectral
typesare difficult targets even on large telescopes due to their
in-trinsic faintness in the optical: they emit most of their fluxin
the red optical and near infrared (NIR) between 0.8 and1.8 µm (the
NIR Y, J and H bands are 0.98-1.1 µm, 1.1-1.4µm and 1.45-1.8 µm).
However, it is the low mass late-type M stars, which are the least
luminous, where the ve-locity amplitude of a terrestrial planet in
the habitable zoneis highest, making them very desirable targets.
Since theflux distribution from M stars peaks sharply in the NIR,
sta-ble high-resolution NIR spectrographs capable of deliver-ing
high RV precision can observe several hundred of thenearest M
dwarfs to examine their planet population.
3.1.1. Fiber-Fed NIR High-Resolution Spectrographs
A number of new fiber-fed stabilized spectrographs arenow being
designed and built for such a purpose: the Hab-itable Zone Planet
finder (Mahadevan et al., 2012) for the10m Hobby Eberly Telescope,
CARMENES (Quirrenbachet al., 2012) for the 3.6m Calar Alto
Telescope and Spirou(Santerne et al., 2013) being considered for
the CFHT. Theinstrumental challenges in the NIR, compared to the
opti-cal, are calibration, stable cold operating temperatures ofthe
instrument, and the need to use NIR detectors. The cali-bration
issues seem tractable (see below). Detection of lightbeyond 1µm
required the use of NIR sensitive detectors likethe Hawaii-2(or
4)RG HgCdTe detectors. These devices arefundamentally different
than CCDs and exhibit effects likeinter-pixel capacitance and much
greater persistence. Initialconcerns about the ability to perform
precision RV mea-surements with these device has largely been
retired withlab (Ramsey et al., 2008) and on sky demonstrations
(Ycaset al., 2012b) with a Pathfinder spectrograph, though care-ful
attention to ameliorating these effects is still necessaryto
achieve high RV precision. This upcoming generation
ofspectrographs, being built to deliver 1-3 m s−1 RV precisionin
the NIR will also be able to confirm many of the planets
3
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detected with TESS and Gaia around low mass stars.
NIRspectroscopy is also a essential tool to be able to
discrimi-nate between giant planets and stellar activity in the
searchfor planets around young active stars (Mahmud et al.,
2011).
3.1.2. Calibration Sources
Unlike iodine in the optical no single known gas
cellsimultaneously covers large parts of the NIR z, Y, J &
Hbands. Thorium Argon lamps, that are so successfully usedin the
optical have very few Thorium emission lines in theNIR, making them
unsuitable as the calibrator of choicein this wavelength regime.
Uranium has been shown toprovide a significant increase in the
number of lines avail-able for precision wavelength calibration in
the NIR. Newlinelists have been published for Uranium lamps
(Redmanet al., 2011, 2012) and these lamps are now in use in
ex-isting and newly commissioned NIR spectrographs. Laserfrequency
combs, which offer the prospects of very highprecision and accuracy
in wavelength calibration, have alsobeen demonstrated with
astronomical spectrographs in theNIR (Ycas et al., 2012b) with
filtering making them suitablefor an astronomical spectrograph.
Generation of combsspanning the entire z-H band regions has also
been demon-strated in the lab (Ycas et al., 2012a). Continuing
devel-opment efforts are aimed at effectively integrating
thesecombs as calibration sources for M dwarf Doppler surveyswith
stabilized NIR spectrographs. Single mode fiber-basedFabry-Pérot
cavities fed by supercontinuum light sourceshave also been
demonstrated by Halverson et al. (2012).To most astronomical
spectrographs the output from thesedevices looks similar to that of
a laser comb, although thefrequency of the emission peaks is not
known innately tohigh precision. Such inexpensive and rugged
devices maysoon be available for most NIR spectrographs, with the
su-perior (and more expensive) laser combs being reserved forthe
most stable instruments on the larger facilities. Whilemuch work
remains to be done to refine these calibrationsources, the
calibration issues in the NIR largely seem to bewithin reach.
3.1.3. Single Mode Fiber-fed Spectrographs
The advent of high strehl ratio adaptive optics (AO) sys-tems at
most large telescopes makes it possible to seriouslyconsider using
a single-mode optical fiber (SMF) to couplethe light from the focal
plane of the telescope to a spectro-graph. Working close to the
diffraction limit enables suchSMF-fed spectrographs to be very
compact while simulta-neously capable of providing spectral
resolution compara-ble or superior to natural seeing spectrographs.
A num-ber of groups are pursuing technology development relat-ing
to these goals (Ghasempour et al., 2012; Schwab et al.,2012; Crepp,
2013). The single mode fibers provide the-oretically perfect
scrambling of the input PSF, further aid-ing in the possibility of
very high precision and compactDoppler spectrometers emerging from
such developmentpaths. While subtleties relating to polarization
state and its
impact on velocity precision remain to be solved, many ofthe
calibration sources discussed above are innately adapt-able to use
with SMF fiber-fed spectrographs. Since theefficiency of these
systems depends steeply on the level ofAO correction, it is likely
that Doppler RV searches target-ing the red optical and NIR
wavelengths will benefit themost.
3.2. Spectroscopic Detection of Planetary Companions
Direct spectroscopic detection of the orbit of non-transiting
planets has finally yielded successful results thisdecade. While
the traditional Doppler technique relies ofdetecting the radial
velocity of the star only, the direct spec-troscopic detection
technique relies on observing the star-planet system in the NIR or
thermal IR (where the planetto star flux ratio is more favorable
than the optical) andobtaining high resolution, very high S/N
spectra to be ableto spectroscopically measure the radial velocity
of both thestar and the planet in a manner analogous to the
detectionof a spectroscopic binary (SB2). The radial velocity
ob-servations directly yield the mass ratio of the
star-planetsystem. If the stellar mass is known (or estimated
well)the planet mass can be determined with no sin i ambigu-ity
despite the fact that these are not transiting systems.The
spectroscopic signature of planets orbiting Tau Boo,51 Peg, and
HD189733 have recently been detected usingthe CRIRES instrument on
the VLT (Brogi et al., 2012,2013; de Kok et al., 2013; Rodler et
al., 2012) and effortsare ongoing by multiple groups to detect
other systems us-ing the NIRSPEC instrument at Keck (Lockwood et
al.,2014). The very high S/N required of this technique lim-its it
to the brighter planet hosts, and to rleatively close-inplanets,
but yields information about mass and planetaryatmospheres that
would be difficult to determine otherwisefor the non-transiting
planets. Such techniques complementthe transit detection efforts
underway and will increase insensitivity with telescope aperture ,
better infrared detec-tors, and more sophisticated analysis
techniques. While wehave focused primarily on planet detection
techniques inthis review article, high resolution NIR spectroscopy
usinglarge future gound based telescopes may also be able to
de-tect astrobiologically interesting molecules (eg. O2)
aroundEarth-analogues orbiting M dwarfs (Snellen et al., 2013).
4. Doppler Measurements from Space
Although there are no current plans to build high-resolution
spectrometers for space missions, this environ-ment might offer
some advantages for extreme precisionDoppler spectroscopy if the
instrument would be in a stablethermal and pressure environment.
Without blurring fromthe Earth’s atmosphere, the point spread
function (PSF)would be very stable and the image size could be
smallmaking it intrinsically easier to obtain high resolution
withan extremely compact instrument. Furthermore, the effectof sky
subtraction and telluric contamination are currentlydifficult
problems to solve with ground-based instruments
4
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and these issues are eliminated with space-based
instru-ments.
5. Transit Detections
At the time of the press run for the Protostars andPlanets IV in
2000, the first transiting extrasolar planet –HD 209458b – had just
been found (Henry et al., 2000;Charbonneau et al., 2000). That
momentous announce-ment, however, was too late for the conference
volume, andPPIV’s single chapter on planet detection was devoted
tofourteen planets detected by Doppler velocity monitoring,of which
only eight were known prior to the June 1998meeting. Progress,
however, was rapid. In 2007, whenthe Protostars and Planets V
volume was published, nearly200 planets had been found with Doppler
radial velocities,and nine transiting planets were then known
(Charbonneauet al., 2007).
In the past several years, the field of transit detection
hascome dramatically into its own. A number of
long-runningground-based projects, notably the SuperWASP
(CollierCameron et al., 2007) and HATNet surveys (Bakos et
al.,2007), have amassed the discovery of dozens of
transitingplanets with high-quality light curves in concert with
ac-curate masses determined via precision Doppler
velocitymeasurements. Thousands of additional transiting plane-tary
candidates have been observed from space. Transittiming variations
(Agol et al., 2005; Holman and Murray,2005) have progressed from a
theoretical exercise to a prac-ticed technique. The Spitzer Space
Telescope (along withHST and ground-based assets) has been employed
to char-acterize the atmospheres of dozens of transiting
extrasolarplanets (Seager and Deming, 2010). An entirely new,
andastonishingly populous, class of transiting planets in themass
range R⊕ < RP < 4R⊕ has been discovered andprobed (Batalha et
al., 2013). Certainly, with each newiteration of the Protostars and
Planets series, the previousedition looks hopelessly quaint and out
of date. Is seemscertain that progress will ensure that this
continues to bethe case.
5.1. The Era of Space-based Transit Discovery
Two space missions, Kepler (Borucki et al., 2010) andCoRoT
(Barge et al., 2008) have both exhibited excellentproductivity, and
a third mission, MOST, has provided pho-tometric transit
discoveries of several previously knownplanets (Winn et al., 2011;
Dragomir et al., 2013). Indeed,Figure 1 indicates that during the
past six years, transitingplanets have come to dominate the roster
of new discover-ies. Doppler velocimetry, which was overwhelmingly
themost productive discovery method through 2006, is
rapidlytransitioning from a general survey mode to an intensive
fo-cus on low-mass planets orbiting very nearby stars (Mayoret al.,
2011) and to the characterization of planets discov-ered in transit
via photometry.
The Kepler Mission, in particular, has been
completelytransformative, having generated, at last rapidly
evolving
100 101 102 103 104Period [Days]
10-6
10-5
10-4
10-3
10-2
10-1
Mas
s Ra
tio [M
/MSun]
Eccentric GiantsHot Jupiters
V E
J
Ungiants
Solar System Satellites
Fig. 3.— Green circles: log10(Msatellite/Mprimary) andlog10(P )
for 634 planets securely detected by the radialvelocity method
(either with or without photometric tran-sits). Red circles:
log10(Msatellite/Mprimary) and log10(P )for the regular satellites
of the Jovian planets in the So-lar System. Gray circles:
log10(Msatellite/Mprimary) andlog10(P ) for 1501 Kepler candidates
and objects of interestin which multiple transiting candidate
planets are associatedwith a single primary. Radii for these
candidate planets, asreported in (Batalha et al., 2013), are
converted to massesassuming M/M⊕ = (R/R⊕)2.06 (Lissauer et al.,
2011a),which is obtained by fitting the masses and radii of the
solarsystem planets bounded in mass by Venus and Saturn. Dataare
from www.exoplanets.org, accessed 08/15/2013.
count, over one hundred planets with mass determinations,as well
as hundreds of examples of multiple transiting plan-ets orbiting a
single host star, many of which are in highlyco-planar,
surprisingly crowded systems (Lissauer et al.,2011b). Taken in
aggregate, the Kepler candidates indicatethat planets with masses
MP < 30M⊕ and orbital periods,P < 100 d are effectively
ubiquitous (Batalha et al., 2011),and as shown in Figure 3, the
distribution of mass ratiosand periods of these candidate planets
are, in many cases,curiously reminiscent of the regular satellites
of the Jovianplanets within our own solar system.
The CoRoT satellite ceased active data gathering in late2012,
having substantially exceeded its three-year designlife. In Spring
of 2013, just after the end of its nomi-nal mission period, the
Kepler satellite experienced a fail-ure of a second reaction wheel,
which brought its high-precision photometric monitoring program to
a prematurehalt. The four years of Kepler data in hand, however,
arewell-curated, fully public, and are still far from being
fullyexploited; it is not unreasonable to expect that they
willyield additional insight that is equivalent to what has
al-ready been gained from the mission to date. Jenkins et al.(2010)
describe the fiducial Kepler pipeline; steady im-provements to the
analysis procedures therein have led tolarge successive increases
in the number of planet candi-
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dates detected per star (Batalha et al., 2013).The loss of the
Kepler and CoRoT spacecraft has been
tempered by the recent approvals of two new space mis-sions. In
the spring of 2013, NASA announced selection ofthe Transiting
Exoplanet Survey Satellite (TESS) Missionfor its Small Explorer
Program. TESS is currently sched-uled for a 2017 launch. It will
employ an all-sky strategyto locate transiting planets with periods
of weeks to months,and sizes down toRp ∼ 1R⊕ (for small parent
stars) amonga sample of 5 × 105 stars brighter than V = 12,
including∼ 1000 red dwarfs (Ricker et al., 2010). TESS is
designedto take advantage of the fact that the most heavily
stud-ied, and therefore the most scientifically valuable,
transitingplanets in a given category (hot Jupiters, extremely
inflatedplanets, sub-Neptune sized planets, etc.) orbit the
bright-est available parent stars. To date, many of these
“fiducial”worlds, such as HD 209458 b HD 149026 b, HD 189733 b,and
Gliese 436 b, have been discovered to transit by photo-metrically
monitoring known Doppler-wobble stars duringthe time windows when
transits are predicted to occur. Bysurveying all the bright stars,
TESS will systematize the dis-covery of the optimal transiting
example planets within ev-ery physical category. The CHEOPS
satellite is also sched-uled for launch in 2017 (Broeg et al.,
2013). It will com-plement TESS by selectively and intensively
searching fortransits by candidate planets in the R⊕ < Rp <
4R⊕size range during time windows that have been identifiedby
high-precision Doppler monitoring of the parent stars.It will also
perform follow-up observations of interestingTESS candidates.
5.2. Transit Detection
The a-priori probability that a given planet can be ob-served in
transit is a function of the planetary orbit, and theplanetary and
stellar radii
Ptr = 0.0045(
AU
a
)(R?+RpR�
)[1+e cos(π/2−ω)
1− e2
],
(3)where ω is the angle at which orbital periastron occurs,such
that ω = 90◦ indicates transit, and e is the orbitaleccentricity. A
typical hot Jupiter with Rp & RJup andP ∼ 3 d, orbiting a
solar-type star, has a τ ∼ 3 hr tran-sit duration, a photometric
transit depth, d ∼ 1%, andP ∼ 10%. Planets belonging to the
ubiquitous super-Earth – sub-Neptune population identified by
Kepler (i.e.,the gray points in Figure 3) are typified by P ∼
2.5%,d ∼ 0.1%, and τ ∼ 6 hr, whereas Earth-sized planetsin an
Earth-like orbits around a solar-type stars present achallenging
combination of P ∼ 0.5%, d ∼ 0.01%, andτ ∼ 15 hr.
Effective transit search strategies seek the optimal trade-off
between cost, sky coverage, photometric precision, andthe median
apparent brightness of the stars under observa-tion. For nearly a
decade, the community as a whole strug-gled to implement genuinely
productive surveys. For aninteresting summary of the early
disconnect between ex-
pectations and reality, see Horne (2003). Starting in
themid-2000s, however, a number of projects began to pro-duce
transiting planets (Konacki et al., 2003; Alonso et al.,2004;
McCullough et al., 2006), and there are now a rangeof successful
operating surveys. For example, the ongoingKelt-North project,
which has discovered 4 planets to date(Collins et al., 2013)
targets very bright 8 < V < 10 starsthroughout a set of 26◦ ×
26◦ fields that comprise ∼12%of the full sky. Among nearly 50,000
stars in this sur-vey, 3,822 targets have RMS photometric precision
betterthan 1% (for 150-sec exposures). A large majority of theknown
transit-bearing stars, however, are fainter than Kelt’sfaint limit
near V ∼ 10. The 10 < V < 12 regime hasbeen repeatedly
demonstrated to provide good prospects forDoppler follow-up and
detailed physical characterization,along with a large number of
actual transiting planets. Inthis stellar brightness regime,
surveys such as HATNet andSuperWASP have led the way. For instance,
HAT-South(Bakos et al., 2013), a globally networked extension of
thelong-running HATNet project, monitors 8.2◦ × 8.2◦ fieldsand
reaches 6 millimagnitude (mmag) photometric preci-sion at 4-minute
cadence for the brightest non-saturatedstars at r ∼ 10.5.
SuperWASP’s characteristics are roughlysimilar, and to date, it has
been the most productive ground-based transit search program.
To date, the highest-precision ground-based exoplane-tary
photometry has been obtained with orthogonal phasetransfer arrays
trained on single, carefully preselected high-value target stars.
Using this technique, (Johnson et al.,2009) obtained 0.47 mmag
photometry at 80-second ca-dency for WASP-10 (V=12.7). By
comparison, with itsspace-borne vantage, Kepler obtained a median
photomet-ric precision of 29 ppm with 6.5 hour cadence on
V=12stars. This is ∼ 2× better than the best
special-purposeground-based photometry, and ∼ 20× better than the
lead-ing ground-based discovery surveys.
Astrophysical false positives present a serious challengefor
wide-field surveys in general and for Kepler in particu-lar, where
a majority of the candidate planets lie effectivelyout of reach of
Doppler characterization and confirmation(Morton and Johnson,
2011). Stars at the bottom of themain sequence overlap in size with
giant planets (Chabrierand Baraffe, 2000) and thus present
near-identical transitsignatures to those of giant planets. Grazing
eclipsing bi-naries can also provide a source of significant
confusion forlow signal-to-noise light curves (Konacki et al.,
2003).
Within the Kepler field, pixel “blends” constitute a ma-jor
channel for false alarms. These occur when an eclipsingbinary,
either physically related or unrelated, shares line ofsight with
the target star. Photometry alone can be usedto identify many such
occurrences (Batalha et al., 2010),whereas in other cases,
statistical modeling of the likeli-hood of blend scenarios (Torres
et al., 2004; Fressin et al.,2013) can establish convincingly low
false alarm proba-bilities. High-profile examples of confirmation
by statis-tical validation include theR = 2.2R⊕ terrestrial
candidateplanet Kepler 10c by (Fressin et al., 2011), as well as
the
6
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planets in the Kepler 62 system (Borucki et al., 2013).
Falsealarm probabilities are inferred to be dramatically lower
forcases where multiple candidate planets transit the same
star.Among the gray points in Figure 3 there is very likely onlya
relatively small admixture of false alarms.
5.3. Results and Implications
Aside from the sheer increase in the number of tran-siting
planets that are known, the string of transit discov-eries over the
past six years have been of fundamentallynovel importance. In
particular, transit detections have en-abled the study of both
planets and planetary system archi-tectures for which there are no
solar system analogs. Abrief tally of significant events logged in
order of discov-ery year might include (i) Gliese 436 b (Gillon et
al., 2007)the first transiting Neptune-sized planet and the first
planetto transit a low-mass star, (ii) HD 17156 b the first
transit-ing planet with a large orbital eccentricity (e=0.69) and
anorbital period (P = 21d) that is substantially larger thanthe 2 d
< P < 5 d range occupied by a typical hot Jupiter(Barbieri et
al., 2007), (iii) CoRoT 7 b (Léger et al., 2009)and Gliese 1214b
(Charbonneau et al., 2009) the first tran-siting planets with
masses in the so-called “super-Earth”regime 1 M⊕ < M < 10 M⊕,
(iv) Kepler 9b and 9c (Hol-man et al., 2010) the first planetary
system to show tan-gible transit timing variations, as well as the
first case oftransiting planets executing a low-order mean motion
reso-nance, (v) Kepler 22b, the first transiting planet with a
sizeand an orbital period that could potentially harbor an
Earth-like environment (Borucki et al., 2012), and (vi) the
Kepler62 system (Borucki et al., 2013), which hosts at least
fivetransiting planets orbiting a K2V primary. The outer
twomembers, Planet “e” with P = 122 d and Planet “f” withP = 267 d,
both have 1.25R⊕ < Rp < 2R⊕, and receiveS = 1.2 ± 0.2S� and S
= 0.4 ± 0.05S� of Earth’s solarflux respectively.
Bulk densities are measured for transiting planets withparent
stars that are bright enough and chromospheri-cally quiet enough to
support Doppler measurement ofMP sin(i), and can also be obtained
by modeling transittiming variations (Fabrycky et al., 2012;
Lithwick et al.,2012). Over 100 planetary densities (mostly for
hotJupiters) have been securely measured. These are plottedin
Figure 4, which hints at the broad outlines of an over-all
distribution. Figure 4 is anticipated to undergo rapidimprovement
over the next several years as more Keplercandidates receive mass
determinations. It appears likely,however, that there exists a very
broad range of planetaryradii at every mass. For example, to within
errors, planetswith MP ∼ 6M⊕ appear to range in radius by a factor
of atleast three. While a substantial number of short-period gi-ant
planets are inflated by unknown energy source(s) (Baty-gin and
Stevenson, 2010), compositional variations are atleast capable of
explaining the observed range of radii forplanets with MP <
0.2MJup (Fortney et al., 2007). Themass-density distribution (and
by extension, the compo-
sition distribution) of extrasolar planets as a function
ofstellocentric distance is an important outcome of the
planetformation process. It is still entirely unclear whether
planetswith P < 100 d that have no solar system analogues are
theproduct of migration processes (Ida and Lin, 2004a) or ofin-situ
formation (Chiang and Laughlin, 2013). More highquality
measurements of transiting planets will be requiredto resolve the
puzzle.
Fig. 4.— Density-Mass diagram for planetswith well-determined
masses and radii. Planetsare color-coded by the equilibrium
temperature,Teq = (R
1/2? T?)/((2a)
1/2(1− e2)1/8), that they wouldhave if they were zero-albedo
black-bodies re-radiatingfrom the full planetary surface area. The
solar systemplanets more massive than Mars are included in the
plottedaggregate. Gray lines show expected ρ(MP ) for
planetarymodels of pure hydrogen-helium, pure water, pure
silicate,and pure iron compositions. Planetary data are
fromwww.exoplanets.org, accessed 08/15/2013.
The large number of candidate multiple transiting planetsystems
indicate that co-planar architectures are the rule forplanets with
P < 100 d in the size range of Rp ∼ 1.5 – 6R⊕ (Moorhead et al.,
2011). The inclination dispersion ofmost candidate systems with two
or more transiting planetsappears to have a median between 1–3◦.
Candidate planetsin multiple-transit systems, furthermore, are
invariably indynamically stable configurations when imbued with
rea-sonable mass-radius relations (Lissauer et al., 2011a). Na-ture
has therefore produced a galactic planetary census thatis
extraordinarily well-suited to detection and characteriza-tion via
the transit method. The advent of the new spacemissions, in concert
with JWST’s potential for atmosphericcharacterization of low-mass
planets (Deming et al., 2009)indicate that transits will remain at
the forefront for decadesto come.
Finally, transit detection is unique in that it democra-tizes
access to cutting-edge research in exoplanetary sci-ence. Nearly
all of the highly-cited ground-based discov-eries have been made
with small telescopes of apertured < 1m. Amateur observers were
co-discoverers of theimportant transits by HD 17156b (Barbieri et
al., 2007),and HD 80606b (Garcia-Melendo and McCullough, 2009),
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and citizen scientists have discovered several planets to datein
the Kepler data under the auspices of the Planet Huntersproject
(Fischer et al., 2012; Lintott et al., 2013; Schwambet al.,
2013)
6. Direct Imaging Techniques
The field of exoplanets is almost unique in astronomi-cal
science in that the subjects are almost all studied indi-rectly,
through their effects on more visible objects, ratherthan being
imaged themselves. The study of the dominantconstituents of the
universe (dark energy and dark matter)through their gravitational
effects is of course another ex-ample. Direct imaging of the
spatially resolved planet isa powerful complement to the other
techniques describedin this chapter. It is primarily sensitive to
planets in wideorbits a > 5 AU, and since photons from the
planets arerecorded directly, the planets are amenable to
spectroscopicor photometric characterization. However, direct
detectionalso represents a staggering technical challenge. If a
twinto our solar system were located at a distance of 10 pc fromthe
Earth, the brightest planet would have only ∼ 10−9 theflux of the
parent star, at an angular separation of 0.5 arc-seconds.
In spite of this challenge, the field has produced a smallnumber
of spectacular successes: the images and spectra ofmassive (>
1000 M⊕) young self-luminous planets. Theadvent of the first
dedicated exoplanet imaging systemsshould lead to rapid progress
and surveys with statisticalpower comparable to ground-based
Doppler or transit pro-grams. In the next decade, space-based
coronagraphs willbring mature planetary systems into reach, and
some day, adedicated exoplanet telescope may produce an image of
anEarth analog orbiting a nearby star.
6.1. Limitations to high-contrast imaging
The greatest challenge in direct imaging is separatingthe light
of the planet from residual scattered light fromthe parent star.
This can be done both optically – remov-ing the starlight before it
reaches the science detector – andin post-processing, using feature
that distinguishes starlightfrom planetary light.
6.1.1. High-contrast point spread function, coronagraphs,and
adaptive optics
Even in the absence of aberrations, the images createdby a
telescope will contain features that will swamp anyconceivable
planet signal. The point spread function (PSF),as the name implies,
is the response of the telescope toan unresolved point source. In
the case of an unaberratedtelescope, the PSF is the magnitude
squared of the Fouriertransform of the telescope aperture function.
For an unob-scured circular aperture, the diffraction pattern is
the dis-tinctive Airy rings. (The one-dimensional equivalent
wouldrepresent the telescope as a top hat function, whose
Fouriertransform is a sinc, giving a central peak and
oscillating
sidelobes.) More complex apertures will have more com-plex
diffraction patterns.
Removing this diffraction pattern is the task of a coron-agraph.
Originally developed by Lyot (1939) to allow smalltelescopes to
study the coronae of the sun, chronographsemploy optical trickery
to remove the light from an on-axisstar while allowing some of the
flux from the off-axis planetto remain. A wide variety of approches
have been devel-oped (Guyon et al., 2006), far too many to
enumerate here,though they can be divided into a broad families.
The clas-sical Lyot coronagraph blocks the on-axis source with a
fo-cal plane mask, followed by a pupil-plane Lyot mask thatblocks
the light diffracted by the focal plane (Lyot,
1939;Sivaramakrishnan et al., 2001). Apodizers operate by
mod-ifying the transmission of the telescope so that the
Fouriertransform has substantially less power in the sidelobes;
anonphysical example would be a telescope whose trans-mission was a
smoothly-varying gaussian, which would re-sult in a purely gaussian
PSF. In more practical designs,apodization is implemented through
binary ”shaped pupil”masks (Kasdin et al., 2003) and sharply reduce
diffrac-tion over a target region at a significant cost in
through-put. Hybrid Lyot approaches use pupil-plane
apodization(Soummer et al., 2011) or complicated focal-plane
masks(Kuchner and Traub, 2002) to boost the performance ofthe
classic Lyot. Phase-induced amplitude apodization usescomplex
mirrors to create the tapered beam needed to sup-press diffraction
without a loss in throughput (Guyon et al.,2005). A particularly
promising new technique creates anoptical vortex in the focal plane
(Nersisyan et al., 2013) re-moving the diffracted light almost
perfectly for an on-axissource in a unobscured aperture. Many more
complex coro-nagraphs exist - see Guyon et al. (2006) for
discussion. Typ-ically, the best coronagraphs remove diffraction
down to thelevel of 10−10 at separations greater than the inner
workingangle (IWA), typically 2− 4λ/D.
Light is also scattered by optical imperfections - wave-front
errors induced by the telescope, camera, or atmo-spheric
turbulence. Even with a perfect coronagraph, atmo-spheric
turbulence, which typically is many waves of phaseaberration
produces a PSF that completely overwhelms anyplanetary signal. Even
in the absence of atmospheric tur-bulence, small wavefront errors
from e.g., polishing markswill still scatter starlight. These can
be partially correctedthrough adaptive optics - using a deformable
mirror (DM),controlled by some estimate of the wavefront, to
correct thephase of the incoming light. In the case of small phase
er-rors, a Fourier relationship similar to that for diffraction
ex-ists between the wavefront and PSF - see Perrin et al. (2003)and
Guyon et al. (2006) for discussion and examples. Auseful figure of
merit for adaptive optics correction is theStrehl ratio, defined as
the ratio of the peak intensity of themeasured PSF to the
theoretical PSF for an equivalent un-aberrated telescope. With
current-generation adaptive op-tics systems, Strehl ratios of
0.4-0.8 are common in K band- meaning that 60-80 percent of the
scattered light remainsuncorrected.
8
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The halo of light scattered by wavefront errors is par-ticularly
troublesome because it does not form a smoothbackground, but is
broken up into a pattern of speck-les. In monochromatic light these
speckles resemble thediffraction-limited PSF of the telescope, and
hence are eas-ily confused with the signal from a planet. As a
result,high-contrast images are usually nowhere near the
Poissonlimit of photon noise but instead limited by these
speck-les. Uncorrected atmospheric turbulence produces a haloof
speckles that rapidly evolve; static or quasi-static wave-front
errors, such as adaptive optics miscalibrations, pro-duce slowly
evolving speckles that mask planetary signals.
6.1.2. Post-processing
These speckle patterns can be partially mitigated in
post-processing. Such PSF subtraction requires two compo-nents.
First, there must be some distinction between a plan-etary signal
and the speckle pattern - some diversity. Ex-amples include
wavelength diversity, where the wavelengthdependence of the speckle
pattern differs from that of theplanet; rotational diversity, in
which the telecope (and as-sociated speckle pattern) rotates with
respect to the planet/ star combination (Marois et al., 2006); or
observations ofa completely different target star. Such reference
PSFs willnever be a perfect match, as the PSF evolves with time,
tem-perature, star brightness, and wavelength. The second
com-ponent needed for effective PSF subtraction is an algorithmthat
can construct the “best” PSF out of a range of possibil-ities. With
a suitable library of PSFs, least-squares fitting(Lafrenière et
al., 2007a) or principal components analy-sis can assemble
synthetic PSFs and enhance sensitivity toplanets by a factor of
10-100.
6.2. Imaging of self-luminous planets
With these techniques applied to current-generation sys-tems,
planets with brightness ∼ 10−5 can be seen at angu-lar separations
of ∼ 1.0 arcseconds. This is far from thelevel of sensitivity
needed to see mature Jupiter-like plan-ets. Fortunately, planets
are available that are much easiertargets. When a planet forms,
signficant gravitational po-tential energy is available. Depending
on the details of ini-tial conditions, a newly-formed giant planet
may have aneffective temperature of 1000-2000 K (Marley et al.,
2007)and a luminosity of 10−5 to 10−6 L� (Fig. 5). As withthe brown
dwarfs, a large fraction of this energy could bereleased in the
near-infrared, bringing the planet into thedetectable range. Such
planets remain detectable for tens ofmillions of years. Several
surveys have targeted young starsin the solar neighborhood for
exoplanet detection (Liu et al.(2010), Lafrenière et al. (2007b),
Chauvin et al. (2010),benefitting from the identification of nearby
young associ-ations composed of stars with ages 8-50 Myr
(Zuckermanand Song, 2004). Most of these surveys have produced
onlynon-detections, with upper limits on the number of giantplanets
as a function of semi-major axis that exclude largenumbers of
very-wide orbit (50 AU) planets.
Fig. 5.— Reproduction of Fig 4 from Marley et al. (2007)showing
the model radius, temperature and luminosity ofyoung Jupiters as a
function of time since the beginningof their formation. Different
colors reflect different plane-tary masses. Dotted lines indicate
“hot start” planets, whereadiabatic formation retains most of the
initial energy andentropy; solid lines indicate “cold start”, where
accretionthrough a shock (as in the standard core accretion
paradigm)results in loss of entropy. In either case, planets are
singnif-icantly easier to detect at young ages.
A handful of spectacular successes have been obtained.One of the
first detections was a 5 Jupiter-mass object thatwas orbiting not a
star but a young brown dwarf, 2M1207B(Chauvin et al., 2004). A
spectacular example of planetarycompanions to a main-sequence star
is the HR8799 multi-planet system (Figure 6). This consists of four
objects neara young F0V star, orbiting in counterclockwise
directions.The object’s luminosities are well-constrained by
broad-band photometry (Marois et al., 2008; Currie et al.,
2011).Estimates of the planetary mass depend on knowledge ofthe
stellar age - thought to be 30 Myr (Marois et al., 2010;Baines et
al., 2012) and initial conditions; for ’hot start’
9
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planets the masses are 3-7 times that of Jupiter. Multi-planet
gravitational interactions provide a further constrainton the mass
(Marois et al., 2010; Fabrycky and Murray-Clay, 2010), excluding
massive brown dwarf companions.Other notable examples of directly
imaged exoplanets in-clude the very young object 1RXS J1609b
(Lafrenière et al.,2010), the cool planet candidate GJ504B
(Kuzuhara et al.,2013), and the planet responsible for clearing the
gap insidethe Beta pictoris disk (Lagrange et al., 2010). A
candidateoptical HST image of an exoplanet was reported
orbitingFomalhaut (Kalas et al., 2008), but very blue colors and
abelt-crossing orbit (Kalas et al., 2013) indicate that what isseen
is likely light scattered by a debris cloud or disk (thatmay still
be associated with a planet).
The photometric detections of self-luminous planetshave
highlighted the complexities of modeling the atmo-spheres of these
objects. Although they are similar tobrown dwarfs, many of the
directly imaged planets havetemperatures that place them in the
transitional region be-tween cloud-dominated L dwarfs and
methane-dominatedT dwarfs - a change that is poorly understood even
for thewell-studied brown dwarfs. Cloud parameters in particularcan
make an enormous difference in estimates of propertieslike
effective temperature and radius (see supplementarymaterial in
Marois et al. (2008) and subsequent discussionin Barman et al.
(2011), Marley et al. (2012), Currie et al.(2011), and discussion
in the chapter by Madhusudhan etal. in this volume.
If a planet can be clearly resolved from its parent star,it is
accessible not only through imaging but also spectro-scopically.
Integral field spectrographs are particularly wellsuited to this,
e.g., Oppenheimer et al. (2013); Konopackyet al. (2013), since they
also capture the spectrum of neigh-boring speckle artifacts, which
can be used to estimatethe speckle contamination of the planet
itself. Spectrashow that the self-luminous planets do (as expected)
havelow gravity and distinct atmospheric structure from
browndwarfs. In some cases, spectra have sufficiently high SNRthat
individual absorption features (e.g., of CO) can beclearly resolved
(Konopacky et al., 2013), allowing directmeasurements of
atmospheric chemistry and abundances(Figure 7).
6.3. Future ground and space-based facilities
Most direct imaging of exoplanets to date has taken placewith
traditional instruments attached to general-purpose AOsystems, such
as the NIRC2 camera on the Keck II tele-scope or NACO on the VLT.
In fact, for most of these ob-servations, the presence or absence
of a coronagraph hashad little effect on sensitivity, which is
dominated by wave-front errors uncorrected by the AO system. Some
sensitivityenhancement has come from dedicated exoplanet
imagingcameras, employing techniques like dual-channel imaging,in
combination with conventional adaptive optics (Nielsenet al., 2013;
Janson et al., 2013). The combination of pyra-mid wavefront sensing
and adaptive secondary mirrors on
Fig. 6.— Near-infrared Keck adaptive optics images ofthe HR8799
system from Marois et al. (2010). Four gi-ant planets, 3 to 7 times
the mass of Jupiter, are visiblein near-infrared emission.The
residual speckle pattern afterPSF subtraction can be seen in the
center of each image.
Fig. 7.— High-resolution spectrum of the extrasolar
planetHR8799c taken with the OSIRIS spectrograph and the
Keckadaptive optics system, reproduced from Konopacky et al.(2013).
Residual speckle noise changes the overall spectralshape (e.g., the
upturn at the long wavelength end) but doesnot inject narrow
features - the CO break is clearly detectedas are many individual
CO and H2O lines, while methaneis absent.
the LBT and Magellan telescopes has shown excellent
high-contrast performance (Skemer et al., 2012).
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However, to significantly increase the number of
imagedexoplanets will require dedicated instruments that
combinevery high-performance adaptive optics, suitable
corona-graphs, and exoplanet-optimized science instruments suchas
low spectral resolution diffraction-limited integral
fieldspectrographs. The first such instrument to become
opera-tional is the Project 1640 coronagraphic IFS (Oppenheimeret
al., 2013), integrated with a 3000-actuator AO systemon the 5-m
Hale telescope. The Subaru Coronagraphic Ex-treme AO System
(SCExAO; Martinache et al., 2012) is a2000-actuator AO system that
serves as a testbed for a widevariety of advanced technologies
including focal-planewavefront sensing and pupil-remapping
coronagraphs. Fi-nally, two facility-class planet imagers will be
operationalin 2014 on 8-m class telescopes - the Gemini Planet
Im-ager (Macintosh et al., 2012) and the VLT SPHERE facility(Beuzit
et al., 2008; Petit et al., 2012). Both have 1500actuator AO
systems, apodized-pupil Lyot coronagraphs,and integral field
spectrographs. (SPHERE also incorpo-rates a dual-channel IR imager
and a high-precision opticalpolarimeter.) Laboratory testing and
simulations predictthat they will achieve on-sky contrasts of
better than 106
at angles of 0.2 arcseconds, though with the limitation
ofrequiring bright stars (I < 8 mag for GPI, V < 12 magfor
SPHERE ) to reach full performance. Both instrumentswill be located
in the southern hemisphere, where the ma-jority of young nearby
stars are located. Simulated surveys(McBride et al., 2011) predict
that GPI could discover 20-50 Jovian planets in a 900-hour
survey.
Direct detection instruments have also been proposed forthe
upcoming 20-40m Extremely Large Telescopes. Theseinstruments
exploit the large diameters of the telescope toachieve extremely
small inner working angles (0.03 arc-seconds or less), opening up
detection of protoplanets innearby star forming regions orbiting at
the snow line (Mac-intosh et al., 2006), or reflected light from
mature giantplanets close to their parent star (Kasper et al.,
2010). Attheir theoretical performance limits, such telescopes
couldreach the contrast levels needed to detect rocky planets inthe
habitable zones of nearby M stars, though reachingthat level may
present insurmountable technical challenges.(Guyon et al.,
2012).
A coronagraphic capability has been proposed for the2.4m AFTA
WFIRST mission (Spergel et al., 2013). Dueto the obscured aperture
and relative thermal stability of thetelescope, it would likely be
limited to contrasts of 10−9
at separations of 0.1 or 0.2 arcseconds, but this would
stillenable a large amount of giant-planet and disk science,
in-cluding spectral charcterization of mature giant planets.
Direct detection of an Earth-analog planet orbiting asolar-type
star, however, will almost certainly require a ded-icated space
telescope using either an advanced corona-graph - still equiped
with adaptive optics - or a formation-flying starshade
occulter.
7. Microlensing
7.1. Planetary Microlensing
7.1.1. Microlensing Basics
A microlensing event occurs when two stars at differentdistances
pass within ∼ 1 mas of each other on the planeof the sky (Gaudi,
2012). Light from the source star ‘S’is bent by the lens star ‘L’,
so that the observer ‘O’ seesthe the image ‘I’ instead of the true
source (see Fig. 8). Ifthe source and the lens are perfectly
aligned along the lineof sight, the source is lensed into a ring
(Chwolson, 1924;Einstein, 1936; Renn et al., 1997), called an
Einstein ringwhose angular size is given by:
θE =√κMLπrel ∼ 0.3 mas (4)
for typical values of the lens mass (ML = 0.5M�), lensdistance
(DL = 6 kpc), and source distance (DS = 8kpc). In Equation 4, πrel
= (1AU/DL) − (1AU/DS) isthe trigonometric parallax between the
source and the lens,and κ = 8.14 mas M−1� .
If the source is offset from the lens by some smallamount, it is
lensed into two images that appear in line withthe source and the
lens, and close to the Einstein ring as inFigure 9. Because the
size of the Einstein ring is so small,the two images of the source
are unresolved and the primaryobservable is their combined
magnification
A =u2 + 2
u√u2 + 4
, (5)
where u is the projected separation between the source andthe
lens as a fraction of the Einstein ring. Since the sourceand the
lens are both moving, u (and so A) is a function oftime.
Fig. 8.— Basic geometry of microlensing.
7.1.2. Types of Planetary Perturbations
If planets are gravitationally bound to a lensing star,
theplanet can be detected if one of the source images passes
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Fig. 9.— Images of a lensed source star. The position of
thesource is indicated by the small circles. The filled ovoidsshow
the lensed images for each source position. The largeblack circle
shows the Einstein ring. The lens star is at theorigin, marked by
the plus.
over or near the position of the planet. This creates a
pertur-bation to the microlensing light curve of the host star.
Be-cause the images generally appear close to the Einstein
ring,microlensing is most sensitive to planets with projected
sep-arations equal to the physical size of the Einstein ring in
thelens plane, rE = θEDL.
Another way to think about this is to consider the
mag-nification map. The magnification of the source by a pointlens
can be calculated for any position in space using Equa-tion 5,
giving a radially symmetric magnification map. Thesource then
traces a path across this map creating a mi-crolensing event whose
magnification changes as a functionof time (and position). The
presence of the planet distortsthe magnification map of the lens
and causes two or morecaustics to appear as shown by the red curves
in Figure 10a.A perfect point source positioned at a point along
the caus-tic curve will be infinitely magnified. In order to detect
theplanet, the source trajectory must pass over or near a
causticcaused by the planet (Mao and Paczynski, 1991; Gould
andLoeb, 1992; Griest and Safizadeh, 1998).
There are two kinds of perturbations corresponding tothe two
sets of caustics produced by the planet. The “plan-etary caustic”
is the larger caustic (or set of caustics) unas-sociated with the
position of the lens star (right side of Fig.10a). The “central
caustic” is much smaller than the plan-etary caustic and is located
at the position of the lens star(left side of Fig. 10a). Figure 10
shows two example sourcetrajectories, their corresponding light
curves, and details ofthe planetary perturbation in a planetary
caustic crossing.As the mass ratio, q, decreases, so does the
duration of theplanetary perturbation. In addition, the detailed
shape of theperturbation depends on the size of the source star
relativeto the size of the Einstein ring, ρ.
7.1.3. Planet Masses from Higher-Order Effects
The fundamental observable properties of the planet arethe mass
ratio between the planet and the lens star, q, andthe projected
separation between the planet and the lens staras a fraction of the
Einstein ring, s. Hence, while q ≤ 10−3definitively identifies the
companion to the lens as a planet,its physical properties cannot be
recovered without an es-timate of ML and DL. However, if θE and r̃E
(the size ofthe Einstein ring in the observer plane) can be
measured, itis possible to obtain measurements of ML and DL (see
Fig.8) and hence, the physical mass and projected separation ofthe
planet: mp = qML and a⊥ = sθEDL. These variablescan be measured
from higher-order effects in the microlens-ing light curve. If
finite-source effects are observed (c.f.Fig. 10e), θE is measured
since ρ = θ?/θE and the angularsize of the source, θ?, can be
determined from the color-magnitude diagram (Yoo et al., 2004).
Finally, as the Earthorbits the Sun, the line of sight toward the
event changesgiving rise to microlens parallax (Gould, 1992; Gould
et al.,1994), allowing a measurement of r̃E:
πE =1AU
r̃E=πrelθE
. (6)
7.1.4. Microlensing Degeneracies and False-Positives
In microlensing the most common degeneracy is thatplanets with
separation s produce nearly identical cen-tral caustics as planets
with separation s−1 (Griest andSafizadeh, 1998). For planetary
caustics, this is not a ma-jor problem since s (where s is larger
than the Einsteinring) produces a “diamond”-shaped caustic whereas
s−1
produces a pair of “triangular” caustics (Gaudi and Gould,1997).
Additional degeneracies arise when higher-order ef-fects such as
parallax and the orbital motion of the lens aresignificant. In such
cases, the exact orientation of the eventon the sky becomes
important and can lead to both discreteand continuous degeneracies
in the relevant parameters (e.g.Gould, 2004; Skowron et al.,
2011).
False positives are rare in microlensing events in whichthe
source crosses a caustic. Because the magnificationdiverges at a
caustic, this produces a discontinuity in theslope of the light
curve, which is very distinctive (see Fig.10). However, in events
without caustic crossings, planetarysignals can be mimicked by a
binary source (Gaudi, 1998;Hwang et al., 2013), orbital motion of
the lens (e.g. Albrowet al., 2000), or even starspots (e.g. Gould
et al., 2013). Of-ten multi-band data can help distinguish these
scenarios asin the case of starspots or lensing of two sources of
differentcolors.
7.2. Microlensing Observations in Practice
The first microlensing searches were undertaken in thelate
1980s, primarily as a means to find Massive CompactHalo Objects (a
dark matter candidate; Alcock et al., 1992;Aubourg et al., 1993).
These searches were quickly ex-panded to include fields toward the
galactic bulge to searchfor planets and measure the mass function
of stars in the
12
-
Fig. 10.— (a) Magnification map for a planet with q =0.001 and s
= 1.188 and a source size ρ = 0.001. The redlines indicate the
caustics. Two example source trajectoriesare shown. The scale is
such that the Einstein ring is a cir-cle of radius 1.0 centered at
(0,0). The planet is locatedat (1.188,0), just outside the Einstein
ring (off the right-hand side of the plot). (b) Light curve
corresponding tothe left-hand source trajectory (a central caustic
crossing).The dotted line shows the corresponding light curve for
apoint lens. (c) Light curve corresponding to the right-handsource
trajectory (a planetary caustic crossing). (d) Detailof (c) showing
the variation in the planetary signal for dif-ferent values of q =
10−3, 10−4, 10−5 (black, red, cyan).(e) The variation in the
planetary signal for different valuesof ρ = 0.001, 0.01, 0.03
(black, red, cyan).
inner galaxy (Paczynski, 1991; Griest et al., 1991). Onemillion
stars must be observed to find one microlensingevent, so the first
surveys focused on simply detecting mi-crolensing events. These
surveys typically observed eachfield between once and a few times
per night. However, thetimescale of the planet is much shorter: a
day or two for aJupiter down to an hour for an Earth-mass planet.
Hence,followup groups target the known microlensing events toobtain
the higher cadence observations necessary to detectplanets.
In practice, it is not possible to followup all microlens-ing
events, so the first priority is placed on the high-magnification
events (A & 50), i.e., the central caustic
crossing events. Not only can the time of peak sensitivity
toplanets be predicted (around the time of maximum magnifi-cation),
but these events are much more sensitive to planetsthan the average
events, giving maximal planet-yield for theavailable resources
(Griest and Safizadeh, 1998).
To date, almost 20 microlensing planets have been pub-lished,
most of them found using the survey+followupmethod and in high
magnification events. Currently themain surveys for detecting
microlensing events are the Opti-cal Gravitational Lens Experiment
(OGLE; Udalski, 2003)and Microlensing Observations in Astrophysics
(MOA;Bond et al., 2004) . Wise Observatory in Israel is also
con-duction a microlensing survey toward the bulge (Gorbikovet al.,
2010; Shvartzvald and Maoz, 2012). Combined thesesurveys now
discover over 2000 microlensing events eachyear. In addition,
several groups are devoted to followingup these events. They are
Microlensing Follow-Up Net-work (µFUN; Gould et al., 2006),
Microlensing Networkfor the Detection of Small Terrestrial
Exoplanets (MiND-STEp; Dominik et al., 2010), Probing Lensing
AnomaliesNETwork (PLANET; Beaulieu et al., 2006), and
RoboNet(Tsapras et al., 2009).
7.3. Microlensing Planet Discoveries
7.3.1. Highlights
The First Microlensing Planet
The first microlensing planet,
OGLE-2003-BLG-235/MOA-2003-BLG-53Lb, was a 2.6MJup planet
discovered in 2003by the OGLE and MOA surveys (Bond et al., 2004).
Al-though it was discovered and characterized by surveys,
thisplanet was found in “followup mode” in which the MOAsurvey
changed its observing strategy to follow this eventmore frequently
once the planetary anomaly was detected.
Massive Planets Around M-dwarfs
Many of the planets discovered by microlensing have largemass
ratios corresponding to Jovian planets. At the sametime, the
microlensing host stars are generally expected tobe M dwarfs since
those are the most common stars in thegalaxy. Specifically, there
are two confirmed examples ofevents for which the host star has
been definitively identi-fied to be an M dwarf hosting a a
super-Jupiter: OGLE-2005-BLG-071 (Udalski et al., 2005; Dong et
al., 2009)and MOA-2009-BLG-387 (Batista et al., 2011). The
ex-istence of such planets is difficult to explain since the
coreaccretion theory of planet formation predicts that
massive,Jovian planets should be rare around M dwarfs (Laughlinet
al., 2004; Ida and Lin, 2005). However, it is possiblethey formed
through gravitational instability and migratedinward (Boss,
2006).
Multi-Planet Systems
Two of the microlensing events that host planets,
OGLE-2006-BLG-109 (Gaudi et al., 2008) and OGLE-2012-BLG-0026 (Han
et al., 2013), have signals from two different
13
-
planets. The OGLE-2006-BLG-109L system is actually ascale model
of our solar system. The planets in this eventare a Jupiter and a
Saturn analog, with both planets at com-parable distances to those
planets around the Sun when thedifference in the masses of the
stars is taken into account.
Free-floating Planets
Because microlensing does not require light to be detectedfrom
the lenses, it is uniquely sensitive to detecting free-floating
planets. Since θE scales as M1/2, free-floatingplanets have
extremely small Einstein rings and hence giverise to short duration
events (. 1 day). Based on the analy-sis of several years of MOA
survey data, Sumi et al. (2011)found that there are two
free-floating Jupiters for every star.
7.3.2. The Frequency of Planets Measured with Mi-crolensing
Figure 11 compares the sensitivity of microlensing toother
techniques, where the semi-major axis has been scaledby the snow
line, asnow = 2.7AU(M?/M�). The “typical”microlensing host is an M
dwarf rather than a G dwarf, sofrom the perspective of the
core-accretion theory of planetformation, the relevant scales are
all smaller. In this theory,the most important scale for giant
planet formation is the lo-cation of the snow line, which depends
on stellar mass (Idaand Lin, 2004b). Microlensing is most sensitive
to planetsat 1 rE, which is roughly 3 times asnow for an M dwarf
(i.e.,asnow ∼ 1 AU and rE ∼ 3 AU).
Fig. 11.— Sensitivity of microlensing compared to
othertechniques. Figure courtesy B. Scott Gaudi and
MatthewPenny.
The frequency, or occurrence rate, of planets can be cal-culated
by comparing the sensitivities of individual eventsto the planets
detected. Gould et al. (2010) analyzed high-magnification
microlensing events observed by µFUN from2005-2008 and found dN/(d
log q d log s) = 0.31+/−0.15
planets per dex2 normalized at planets with Saturn mass-ratios.
Cassan et al. (2012) also calculated the frequencyof planets using
events observed by PLANET, includ-ing both high and low
magnification events. They founda similar planet frequency of dN/(d
log a d logmp) =10−0.62±0.22(mp/MSat)
0.73±0.17 normalized at Saturn-masses and flat as a function of
semi-major axis. Figures8 and 9 in Gould et al. (2010) compare
their result to theresults from radial velocity for solar-type
stars (Cumminget al., 2008; Mayor et al., 2009) and M dwarfs
(Johnsonet al., 2010b).
7.4. The Future of Microlensing
7.4.1. Second-Generation Microlensing Surveys
Advances in camera technology now make it possible tocarry out
the ideal microlensing survey: one that is simulta-neously able to
monitor millions of stars while also attain-ing a∼ 15 minute
cadence. Both OGLE and MOA have re-cently upgraded to larger
field-of-view cameras (Sato et al.,2008; Soszyński et al., 2012).
They have teamed up withWise Observatory in Israel to continuously
monitor a fewof their fields (Shvartzvald and Maoz, 2012). In
addi-tion, the Korea Microlensing Telescope Network (KMT-Net; Park
et al., 2012) is currently under construction.This network consists
of three identical telescopes in Chile,Australia, and South Africa,
which will conduct a high-cadence microlensing survey toward the
galactic bulge. Asthese second-generation surveys get established,
they willdominate the microlensing planet detections and the bulkof
the detections will shift to planetary caustic crossings.Although
high-magnification events are individually moresensitive to
planets, they are very rare compared to low-magnification events.
Hence, the larger cross-section of theplanetary caustics will make
low-magnification events thedominant channel for detecting planets
in the new surveys.
7.4.2. Space-Based Microlensing
The next frontier of microlensing is a space-based sur-vey,
which has the advantages of improved photometric pre-cision, the
absence of weather, and better resolution. Theimproved resolution
that can be achieved from space is amajor advantage for
characterizing the planets found by mi-crolensing. In ground-based
searches the stellar density inthe bulge is so high that unrelated
stars are often blendedinto the 1′′ PSF. This blending makes it
impossible to accu-rately measure the flux from the lens star, and
hence unlesshigher-order microlensing effects are observed, it is
difficultto know anything about the lens. In space, it is possible
toachieve a much higher resolution that resolves this blend-ing
issue, allowing an estimate of the lens mass based on itsflux and
hence, a measurement of true planet masses ratherthan mass
ratios.
The first microlensing survey satellite was proposed inBennett
and Rhie (2000, 2002). Currently, a microlens-ing survey for
exoplanets has been proposed as a secondaryscience project for the
Euclid mission (Penny et al., 2012;
14
-
Beaulieu et al., 2013) and is a major component of theWFIRST
mission (Spergel et al., 2013). The WFIRST mis-sion is expected to
detect thousands of exoplanets beyondthe snowline (Spergel et al.,
2013). The parameter spaceprobed by this mission is complementary
to that probedby the Kepler mission, which focused on detecting
transitsfrom close-in planets (see Fig. 11).
8. Astrometry
8.1. Introduction
Steady advances in the 18th century improved the pre-cision of
stellar position measurements so that it was pos-sible to measure
the proper motions of stars, their paral-lax displacements due to
Earth’s motion around the Sun,and orbital motion caused by the
gravitational tug of stel-lar companions (Perryman, 2012). While
the impact of as-trometry on exoplanet detection has so far been
limited, thetechnique has enormous potential and is complementary
toother methods (Gatewood, 1976; Black and Scargle, 1982;Sozzetti,
2005). Astrometry is most sensitive to wider or-bits, because the
center of mass displacement amplitudeincreases with orbital period.
As a result, detectable or-bital periods are typically several
years. The need for mea-surement stability and precision over such
long time base-lines has been a challenging requirement for
currently avail-able instruments. Fortunately, with the successful
launch ofthe Gaia satellite, the prospects for space-based
astrometricplanet searches are good.
8.1.1. Parametrization of orbital motion
The term astrometry refers to the measurement of a
star’sposition relative to the background sky, i.e., an
astrometricorbit corresponds to the barycentric motion of a star
causedby an invisible companion. This motion follows Kepler’slaws
and is parametrized by the period P , the eccentricitye, the time
of periastron passage T0, its inclination relativeto the sky plane
i, the longitude of periastron ω, the lon-gitude of the ascending
node Ω, and the semi-major axisa1 expressed in angular units (Fig.
12). The Thiele-Innesconstants A,B, F,G are commonly used instead
of the pa-rameters a1, ω, Ω, i, because they linearize the orbit
term inthe general expression for an astrometric signal Λ
measuredalong an axis determined by the angle ψ
Λ = (∆α? + µα? t) cosψ + (∆δ + µδ t) sinψ +$Πψ
+ (BX +GY ) cosψ + (AX + F Y ) sinψ,
(7)
where $ is the parallax, Πψ is the parallax factor along ψ,X and
Y are the rectangular coordinates (Hilditch, 2001)
X = cosE − e Y =√
1− e2 sinE, (8)
and E is the eccentric anomaly. This relation includes
co-ordinate offsets in the equatorial system (∆α?,∆δ),
propermotions (µα? , µδ), parallactic motion, and orbital motion.It
can be applied to both one and two-dimensional measure-ments made
by Hipparcos, Gaia, or interferometers.
y (E)
zp
n
x(N)
mi
ω
Ω
θ
Fig. 12.— Illustration of the orbit described by a star (m)about
the barycenter located at the origin. The observer seesthe sky
plane defined by the x-y axes from below along thez axis. The
angles i, ω, Ω, Θ, the ascending node n, andthe periastron position
p are indicated. By convention, x isNorth and y is East. Figure
from Sahlmann (2012).
8.1.2. Signal dependence on mass and distance
The semi-major axis ā1 of a star’s barycentric orbit isrelated
to the stellar mass m1, the mass of the companionm2, and the
orbital period by Kepler’s third law (SI units)
4π2ā31P 2
= GM3P
(M∗ +MP )2, (9)
where G is the gravitational constant. The relation be-tween
angular and linear semi-major axes is proportional tothe parallax,
a1 ∝ $ ā1, thus the orbit’s apparent angularsize decreases
reciprocally with the system’s distance fromEarth. The value of a1
determines the semi-amplitude of theperiodic signal we intend to
detect with astrometric mea-surements. Figure 13 shows the minimum
astrometric sig-nature a1,min derived from Eq. 9 for planets listed
in the ex-oplanets.org database (Wright et al., 2011) on June 1,
2013,that have an entry for distance, star mass, orbital period,and
planet mass, where we assumed circular orbits. For ra-dial velocity
planets, a1,min is a lower bound because weset sin i = 1. The
spread at a given period originates in dif-fering distances, star
masses, and planet masses. Figure 13illustrates the typical signal
amplitudes for the known exo-planet population and highlights that
only a small fractionof known planets is accessible with a
measurement preci-sion of 1 milli-arcsec (mas). It also shows that
an improve-ment by only one order of magnitude in precision
wouldset astrometry over the threshold of routine exoplanet
de-tection.
8.1.3. Scientific potential
The motivation for using astrometry to carry out exo-planet
searches is founded in the rich and complementaryorbital
information provided by this technique. Astromet-ric measurements
determine the value of m32/(m1+ m2)
2,thus if the host star mass is known, then planet mass m2can be
estimated without the sin i ambiguity of radial ve-locity
measurements. An astrometric study of a statisti-
15
-
0.01 0.1 1 10 100
Period (year)
10-6
10-510-410-3
0.01
0.1
1
a1,min
(m
illi-
arc
sec)
Me
V E
Ma
JS
UN
Fig. 13.— Minimum astrometric signature of the host staras a
function of orbital period for 570 planets (grey circles).For
reference, the astrometric signatures of a solar-mass starlocated
at a distance of 10 pc caused by the solar systemplanets are shown
with black circles and labelled with theplanet initials.
cal sample of exoplanets could therefore accurately deter-mine
the planet mass function and help to refine theoriesof planet
formation. Equation 9 implies that any orbitalconfiguration creates
an astrometric signal and the ampli-tude increases with orbital
period (see the trend in Fig. 13),making astrometry an ideal
technique for the study of plan-ets on long-period orbits. Because
the technique measuresthe photocenter, it is sensitive to the
detection of planetsaround fast rotating stars with broad spectral
lines or aroundvery faint objects like brown dwarfs. There may also
be areduced sensitivity to stellar activity compared to radial
ve-locity or photometric measurements (Eriksson and Linde-gren,
2007; Lagrange et al., 2011). Since activity is cur-rently
hampering the detection of Earth-mass planets (e.g.,Dumusque et al.
2012), astrometry may hold a distinct ad-vantage for future
searches, although the precision neededto detect Earth-like planets
around the closest stars is atthe level of 1 micro-arcsecond.
Astrometry is applicable toplanet searches around nearby stars of
various masses andages, with benefits for the study of the planet
mass function,of long-period planets, and of planets around active
stars.
8.2. Techniques and Instruments
The precision σ of an astrometric measurement is funda-mentally
limited by the ability to measure an image positionon a detector.
In the diffraction limit, it is therefore relatedto the wavelength
λ, the aperture size D, and the signal-to-noise S/N, typically
limited by photon noise S/N∼
√Np
σ ∝ 1S/N
λ
D, (10)
thus, the achievable astrometric precision improves with
theaperture size. For observations from the ground, the tur-bulence
in the Earth’s atmosphere above the telescope isthe dominant error
source. It can be mitigated by modelingof seeing-limited
observations (Lazorenko and Lazorenko,
2004), by the use of adaptive optics (Cameron et al., 2009),and
with off-axis fringe tracking in dual-field interferom-etry (Shao
and Colavita, 1992). Space-borne instrumentsavoid atmospheric
perturbations altogether and give accessto nearly
diffraction-limited observations, thus are ideal forhigh-precision
astrometry work. Regardless of how the datawere collected, the
number of free astrometric parametersof a system with n planets is
5 + n × 7, i.e., at least 12(see Eq. 7), compared to 1 + n × 5
parameters for a radialvelocity orbit adjustment (Wright and
Howard, 2009). Toobtain a robust solution and to minimize parameter
corre-lations, for instance between proper, parallactic, and
orbitalmotion, a minimum timespan of one year and
appropriatesampling of the orbital period are required.
8.2.1. Ground-based astrometry
Repeated imaging of a target and the measurement of itsmotion
relative to background sources is a basic astromet-ric method and
several planet search surveys use seeing-limited optical imaging
with intermediate and large tele-scopes (Pravdo and Shaklan, 1996;
Boss et al., 2009). Ac-curacies of better than 0.1 mas have been
achieved with thismethod (Lazorenko et al., 2009), which satisfies
the per-formance improvement necessary for efficient planet
detec-tion. Adaptive-optics assisted imaging is also being used,for
instance for a planet search targeting binaries with sep-arations
of a few arcseconds (Röll et al., 2011). An op-tical
interferometer realizes a large effective aperture sizeby combining
the light of multiple telescopes that trans-lates into an
achievable precision of 0.01 milliarcseconds inthe relative
separation measurement of two stars typicallyless than 1′ apart
(Shao and Colavita, 1992). Several obser-vatories have implemented
the necessary infrastructure andare pursuing astrometric planet
search programmes (Laun-hardt et al., 2008; Muterspaugh et al.,
2010; Woillez et al.,2010; Sahlmann et al., 2013b). Similarly, Very
Long Base-line Radio Interferometry is a promising method for
tar-geting nearby stars sufficiently bright at radio
wavelengths.(Bower et al., 2009).
8.2.2. Astrometry from space
Space astrometry was firmly established by the Hippar-cos
mission that operated in 1989-1992 and resulted in thedetermination
of positions, proper motions, and absoluteparallaxes at the 1 mas
level for 120 000 stars (Perrymanet al., 1997). The satellite’s
telescope had a diameter ofonly 29 cm and scanned the entire
celestial sphere severaltimes to construct a global and absolute
reference frame.However, Hipparcos data do not have the necessary
preci-sion to determine the astrometric orbits of the majority
ofknow exoplanets. On a smaller scale but with slightly
betterprecision, the Hubble space telescope fine guidance sensorhas
made stellar parallax and orbit measurements possible(Benedict et
al., 2001). Because the Stellar InterferometryMission (Unwin et
al., 2008) was discontinued, Gaia is thenext space astrometry
mission capable of detecting extraso-
16
-
lar planets.
8.3. Results from Astrometry
8.3.1. Combination with radial velocities
For a planet detected with radial velocities (RV), five outof
seven orbital parameters are constrained. The two re-maining
parameters, the inclination i and Ω, can be deter-mined by
measuring the astrometric orbit. The knowledgeof the RV parameters
(or the high weight of RV measure-ments) leads to a significant
reduction of the required S/Nfor a robust astrometric detection.
Second, even an astro-metric non-detection carries valuable
information, e.g., anupper limit to the companion mass. Therefore,
this type ofcombined analysis is so far the most successful
applicationof astrometry in the exoplanet domain. Hipparcos
astrom-etry yielded mass upper limits of RV planets (Perrymanet
al., 1996; Torres, 2007; Reffert and Quirrenbach, 2011)and revealed
that, in rare cases, brown dwarf (Sahlmannet al., 2011a) or stellar
companions (Zucker and Mazeh,2001) are mistaken for RV planets
because their orbitalplanes are seen with small inclinations.
Similarly, the Hub-ble fine guidance sensor was used to determine
the orbitsand masses of brown dwarf companions to Sun-like
starsinitially detected with RV (Martioli et al., 2010; Benedictet
al., 2010) and ground-based imaging astrometry yieldeda mass upper
limit of ∼ 3.6MJ to the planet around GJ317(Anglada-Escudé et al.,
2012). Sahlmann et al. (2011b)(Fig. 14) used Hipparcos data to
eliminate low-inclinationbinary systems mimicking brown dwarf
companions de-tected in a large RV survey, revealing a mass range
wheregiant planets and close brown dwarf companions aroundSun-like
stars are extremely rare.
M2 sin i (Jupiter mass)
Cum
ulat
ive
dist
ribut
ion
VoidGiant Planets
Brown dwarfcompanions
13 26 39 52 65 780
0.2
0.4
0.6
0.8
1
Fig. 14.— The minimum mass distribution of substellarcompanions
within 10 AU of Sun-like stars from the CoralieRV survey after
constraining the orbital inclinations withHipparcos astrometry.
8.3.2. Independent discoveries
Working towards the goal of exoplanet detection, opticalimaging
surveys have succeeded in measuring the orbits oflow-mass binaries
and substellar companions to M dwarfs(Pravdo et al., 2005; Dahn et
al., 2008), relying on astro-metric measurements only.
Interferometric observations re-
vealed the signature of a Jupiter-mass planet around a starin an
unresolved binary (Muterspaugh et al., 2010), which,if confirmed
independently, represents the first planet dis-covered by
astrometry. Recent improvements of imagingastrometry techniques
towards 0.1 mas precision made thediscovery of a 28 MJ companion to
an early L dwarf pos-sible (Fig. 15) and demonstrated that such
performance canbe realised with a single-dish telescope from the
ground.
42024
Offset in Right Ascension (mas)
8
6
4
2
0
2
4
Off
set
in D
ecl
inati
on (
mas)
Fig. 15.— The barycentric orbit of the L1.5 dwarf DENIS-P
J082303.1-491201 caused by a 28 Jupiter mass compan-ion in a 246
day orbit discovered through ground-basedastrometry with an optical
camera on an 8 m telescope(Sahlmann et al., 2013a).
8.4. The Future
Without a doubt, our expectations are high for the Gaiamission
which was launched on 19 December 2013. Gaia isa cornerstone
mission of the European Space Agency thatwill implement an all-sky
survey of an estimated billionstellar objects with visible
magnitudes of 6–20 (Perrymanet al., 2001; de Bruijne, 2012). On
average, the astrometryof a star will be measured 70 times over the
mission life-time of five years with a single measurement precision
of∼0.02-0.05 mas for stars brighter than ∼14th magnitude.Another
look at Fig. 13 shows that hundreds of known ex-oplanet systems
will be detectable and it is expected thatGaia will discover
thousands of new exoplanets (Casertanoet al., 2008), yielding a
complete census of giant exoplan-ets in intermediate-period orbits
around nearby stars. Thesight of astrometric orbits caused by
planets around starswill then become just as common as radial
velocity curvesand dips in light-curves are today. Assuming that it
will
17
-
perform as planned, Gaia will therefore add astrometry tothe
suite of efficient techniques for the study of exoplanetpopulations
and will help us to advance our understandingof (exo-)planet
formation. It will also pave the way forfuture space astrometry
missions aiming at detecting theEarth-like planets around nearby
stars (Malbet et al., 2012).
At the same time, ground-based surveys will remaincompetitive
because they offer long lifetimes, schedul-ing flexibility, and
access to targets not observable oth-erwise. They are also
necessary for technology develop-ment and demonstration. The
upcoming generation of sub-mm/optical interferometers and
telescopes will have largerapertures and wide-field image
correction, and hence pro-vide us with even better astrometric
performance and newopportunities for exoplanet science.
9. Statistical Distributions of Exoplanet Properties
In this section, we review and interpret the major statis-tical
properties of extrasolar planets. We focus primarilyon results from
RV and transit surveys since they have pro-duced the bulk of the
discovered planets. Fig. 16 showsknown planets with measured masses
and semi-major axes(projected for microlensing planets). The major
archetypesof well-studied planets—cool Jupiters in ∼1–5 AU
orbits,hot Jupiters in sub-0.1 AU orbits, and
sub-Neptune-sizeplanets orbiting within 1 AU—are all represented,
althoughtheir relative frequencies are exaggerated due to
differingsurvey sizes and yields. For more thorough reviews of
ex-oplanet properties, the reader is directed to the
literature(Howard, 2013; Cumming, 2011; Marcy et al., 2005; Udryand
Santos, 2007).
9.1. Abundant, close-in small planets
Planets intermediate in size between Earth and Nep-tune are
surprisingly common in extrasolar systems, butnotably absent in our
Solar System. The planet size andmass distributions (Fig. 17)
demonstate that small plan-ets substantially outnumber large ones,
at least for close-in orbits. Doppler surveys using HIRES at Keck
Observa-tory (Howard et al., 2010)